Chapter 29, Problem 3Q

To determine

Part(a)To state:

Does the molecule of ${\text{H}}_{\text{2}}$ have a permanent dipole moment.

Answer to Problem 3Q

Solution:

No, the molecule of ${\text{H}}_{\text{2}}$ does not have a permanent dipole moment.

Explanation of Solution

Given:

The chemical formula of Hydrogen molecule is ${\text{H}}_{\text{2}}$.

The molecule of ${\text{H}}_{\text{2}}$ has two electrons and both the electrons are in the ground state orbital with the one having spin up and the other having spin down, because, according to the Pauli’s exclusion principle, no two electrons can occupy the same state.

In the ${\text{H}}_{\text{2}}$ molecule, an electron’s spin cannot flip, because, then the electron would be occupying the same state as the other electron violating the Pauli’s exclusion principle.

As the two electrons are not in the same orbital, the proton spin flips from aligned to anti-aligned, but, proton is massive particle and fully localized, thus, the spin-spin coupling between them is insignificant.

To determine

Part (b)To state:

Does the molecule of ${\text{O}}_{\text{2}}$ have a permanent dipole moment.

Answer to Problem 3Q

Solution:

No, the molecule of ${\text{O}}_{\text{2}}$ does not have a permanent dipole moment.

Explanation of Solution

Given:

The chemical formula of oxygen molecule is ${\text{O}}_{\text{2}}$.

The molecule of ${\text{O}}_{\text{2}}$ has two electrons and both the electrons are in the ground state orbital with the one having spin up and the other having spin down, because, according to the Pauli’s exclusion principle, no two electrons can occupy the same state.

In the ${\text{O}}_{\text{2}}$ molecule, an electron’s spin cannot flip, because, then the electron would be occupying the same state as the other electron violating the Pauli’s exclusion principle.

As the two electrons are not in the same orbital, the proton spin flips from aligned to anti-aligned, but, proton is massive particle and fully localized, thus, the spin-spin coupling between them is insignificant.

To determine

Part (c)To state:

Does the molecule of ${\text{H}}_{\text{2}}\text{O}$ have a permanent dipole moment.

Answer to Problem 3Q

Solution:

Yes, the molecule of ${\text{H}}_{\text{2}}\text{O}$ have a permanent dipole moment.

Explanation of Solution

Given:

The chemical formula of water molecule is ${\text{H}}_{\text{2}}\text{O}$.

The chemical formula ${\text{H}}_{\text{2}}\text{O}$ represents water and it is polar in nature. The structure of water molecule has a triangular structure with oxygen atom as vertex. The oxygen atom also has two pair of electrons. The pairs of electron are closer to the oxygen atom than the electrons that are bonded by the sigma bonding to the hydrogen atom. Therefore, they require more space

The polar nature of the water molecule is due to the difference in electronegativity which leads to the occurrence of the bond dipole moment. The dipole moment points from each H atom to the O atom, because, the dipole always points from the negative to the positive direction.

The Hydrogen ion is positive ion, that is, ${\text{H}}^{\text{+}}$ and the Oxygen ion is negative ion, that is, ${\text{O}}^{\text{-}}$. This makes the oxygen partially negative and each hydrogen partially positive.

Therefore, a large molecular dipole is formed pointing from a positive space between the two hydrogen atoms to the negative region of the oxygen atom.

Hence, ${\text{H}}_{\text{2}}\text{O}$ have a permanent dipole moment.